Finite Group Databasebeta

← C2×#22591007 #32156178

Subgroups — C2×#22591007 #32156178

Order 18176.

3718 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556110C211yesmaximal, characteristic
2C22×C4×C22⋊D71C211yesmaximal, characteristic
3C22×C4⋊C4×D71C211yesmaximal, characteristic, complemented
4#22591007C2116yesmaximal, direct product factor
5C2×#17985896C211yesmaximal, characteristic, complemented
6C2×#17985895C211yesmaximal, characteristic, complemented
7C2×#17985892C211yesmaximal, characteristic, complemented
8C2×#17985887C211yesmaximal, characteristic, complemented
9C2×#17985884C211yesmaximal, characteristic, complemented
10C2×#17985880C211yesmaximal, characteristic, complemented
11C2×#17985875C211yesmaximal, characteristic
12C2×#17985872C211yesmaximal, characteristic, complemented
13C2×#17985870C211yesmaximal, characteristic, complemented
14C2×#17985861C211yesmaximal, characteristic, complemented
15C2×#17985846C211yesmaximal, characteristic, complemented
16C2×#385×C71C211yesmaximal, characteristic, complemented
17C23×C22⋊D71C2211yescharacteristic
18C23×C4×D71C2211yescharacteristic
19C23×C4×D71C2211yescharacteristic
20C23×C4×D71C2211yescharacteristic
21C2×#14556110C4116yescomplemented
22C2×#14556110C2218yes—
23C2×C4×C22⋊D71—28no—
24C2×C4×C22⋊D71C2218yes—
25C22×C4⋊Dic71C2211yescharacteristic
26C22×C4⋊Dic71C2211yescharacteristic
27C22×Dic71⋊C4C2211yescharacteristic
28C22×Dic71⋊C4C2211yescharacteristic
29C22×Dic71⋊C4C2211yescharacteristic
30C22×Dic71⋊C4C2211yescharacteristic
31C22×Dic71⋊C4C2211yescharacteristic
32C2×C4⋊C4×D71—28no—
33C2×C4⋊C4×D71C2218yescomplemented
34C22×C22⋊Dic71C2211yescharacteristic
35C22×C22⋊Dic71C2211yescharacteristic
36C22×C22⋊Dic71C2211yescharacteristic
37C22×(C2×D71)⋊C4C2211yescharacteristic
38C22×(C2×D71)⋊C4C2211yescharacteristic
39C22×(C2×D71)⋊C4C2211yescharacteristic
40C22×C4×Dic71C2211yescharacteristic
41C22×C4×Dic71C2211yescharacteristic
42C22×C4×Dic71C2211yescharacteristic
43#17985896C2218yescomplemented
44#17985895C2218yescomplemented
45#17985892C2218yescomplemented
46#17985887C2218yescomplemented
47#17985884C2218yescomplemented
48#17985880C2218yescomplemented
49#17985875C2218yes—
50#17985872C2218yescomplemented
51#17985870C2218yescomplemented
52#17985861C2218yescomplemented
53#17985846C2218yescomplemented
54C2×C71⋊#95C2211yescharacteristic
55C2×C71⋊#95C2211yescharacteristic
56C2×C71⋊#95C2211yescharacteristic
57C2×C71⋊#95C2211yescharacteristic
58C2×C71⋊#95C2211yescharacteristic
59C2×C71⋊#95C2211yescharacteristic
60C2×C71⋊#95C2211yescharacteristic
61C2×C71⋊#95C2211yescharacteristic
62C24×C4×C71C2211yescharacteristic
63C22×C4⋊C4×C71C2211yescharacteristic
64C22×C4⋊C4×C71C2211yescharacteristic
65C22×C22⋊C4×C71C2211yescharacteristic
66C22×C22⋊C4×C71C2211yescharacteristic
67#385×C71C2218yescomplemented
68C2×#95×C71C2211yescharacteristic
69C2×#95×C71C2211yescharacteristic
70C24×D71C2311yescharacteristic
71C22×C22⋊D71—24no—
72C22×C22⋊D71—24no—
73C22×C22⋊D71C2×C418yes—
74C22×C22⋊D71C2314yes—
75C23×Dic71C2311yescharacteristic
76C23×Dic71C2311yescharacteristic
77C23×Dic71C2311yescharacteristic
78C23×Dic71C2311yescharacteristic
79C23×Dic71C2311yescharacteristic
80C23×Dic71C2311yescharacteristic
81C23×Dic71C2311yescharacteristic
82C22×C4×D71—24no—
83C22×C4×D71—24no—
84C22×C4×D71—24no—
85C22×C4×D71—42no—
86C22×C4×D71—42no—
87C22×C4×D71—42no—
88C22×C4×D71—42no—
89C22×C4×D71C2×C418yescomplemented
90C22×C4×D71D418yes—
91C22×C4×D71C2314yes—
92C22×C4×D71C2314yes—
93C22×C4×D71C2314yes—
94#14556110C2×C4164yescomplemented
95C4×C22⋊D71—232no—
96C2×C4⋊Dic71—24no—
97C2×C4⋊Dic71C2×C418yescomplemented
98C2×C4⋊Dic71C2314yes—
99C2×C4⋊Dic71C2314yes—
100C2×Dic71⋊C4—24no—
101C2×Dic71⋊C4—24no—
102C2×Dic71⋊C4—24no—
103C2×Dic71⋊C4—42no—
104C2×Dic71⋊C4C2×C418yescomplemented
105C2×Dic71⋊C4C2314yes—
106C2×Dic71⋊C4C2314yes—
107C2×Dic71⋊C4C2314yes—
108C2×Dic71⋊C4C2314yes—
109C2×Dic71⋊C4C2314yes—
110C4⋊C4×D71—232no—
111C2×C22⋊Dic71—24no—
112C2×C22⋊Dic71—42no—
113C2×C22⋊Dic71C2×C418yescomplemented
114C2×C22⋊Dic71C2314yes—
115C2×C22⋊Dic71C2314yes—
116C2×C22⋊Dic71C2314yes—
117C2×(C2×D71)⋊C4—24no—
118C2×(C2×D71)⋊C4—24no—
119C2×(C2×D71)⋊C4C2×C418yescomplemented
120C2×(C2×D71)⋊C4C2314yes—
121C2×(C2×D71)⋊C4C2314yes—
122C2×(C2×D71)⋊C4C2314yes—
123C2×C4×Dic71—24no—
124C2×C4×Dic71—42no—
125C2×C4×Dic71—42no—
126C2×C4×Dic71C2314yes—
127C2×C4×Dic71C2314yes—
128C2×C4×Dic71C2314yes—
129C71⋊#95C2314yes—
130C71⋊#95C2314yes—
131C71⋊#95C2314yes—
132C71⋊#95C2314yes—
133C71⋊#95C2314yes—
134C71⋊#95C2314yes—
135C71⋊#95C2314yes—
136C71⋊#95C2314yes—
137C25×C71C2311yescharacteristic
138C23×C4×C71—24no—
139C23×C4×C71—42no—
140C23×C4×C71—42no—
141C23×C4×C71C2311yescharacteristic
142C23×C4×C71C2311yescharacteristic
143C23×C4×C71C2311yescharacteristic
144C23×C4×C71C2311yescharacteristic
145C23×C4×C71C2311yescharacteristic
146C23×C4×C71C2311yescharacteristic
147C23×C4×C71C2314yes—
148C2×C4⋊C4×C71—24no—
149C2×C4⋊C4×C71—42no—
150C2×C4⋊C4×C71C2314yes—
151C2×C4⋊C4×C71C2314yes—
152C2×C22⋊C4×C71—42no—
153C2×C22⋊C4×C71C2×C418yescomplemented
154C2×C22⋊C4×C71C2314yes—
155C2×C22⋊C4×C71C2314yes—
156#95×C71C2314yes—
157#95×C71C2314yes—
158C23×D71—22no—
159C23×D71—22no—
160C23×D71—22no—
161C23×D71—22no—
162C23×D71C22×C414yes—
163C23×D71C2×D414yes—
164C23×D71#4114yes—
165C23×D71C2412yes—
166C2×C22⋊D71—232no—
167C2×C22⋊D71—28no—
168C2×C22⋊D71—28no—
169C2×C22⋊D71C22×C4116yes—
170C22×Dic71—22no—
171C22×Dic71—22no—
172C22×Dic71—22no—
173C22×Dic71—22no—
174C22×Dic71—22no—
175C22×Dic71—22no—
176C22×Dic71—22no—
177C22×Dic71—22no—
178C22×Dic71—22no—
179C22×Dic71—22no—
180C22×Dic71—22no—
181C22×Dic71—22no—
182C22×Dic71—22no—
183C22×Dic71—22no—
184C22×Dic71—22no—
185C22×Dic71—22no—
186C22×Dic71—22no—
187C22×Dic71C22×C414yes—
188C22×Dic71C22×C414yes—
189C22×Dic71C22×C414yes—
190C22×Dic71C2×D414yes—
191C22×Dic71C2412yes—
192C22×Dic71C2412yes—
193C22×Dic71C2412yes—
194C22×Dic71C2412yes—
195C22×Dic71C2412yes—
196C22×Dic71C2412yes—
197C22×Dic71C2412yes—
198C2×C4×D71—232no—
199C2×C4×D71—28no—
200C2×C4×D71—28no—
201C2×C4×D71—28no—
202C2×C4×D71—416no—
203C2×C4×D71—44no—
204C2×C4×D71—44no—
205C2×C4×D71—44no—
206C2×C4×D71—44no—
207C2×C4×D71—416no—
208C2×C4×D71C22×C4116yescomplemented
209C2×C4×D71C2×D4116yes—
210C4⋊Dic71—28no—
211C4⋊Dic71C22×C4116yescomplemented
212Dic71⋊C4—28no—
213Dic71⋊C4—28no—
214Dic71⋊C4—28no—
215Dic71⋊C4—44no—
216Dic71⋊C4C22×C4116yescomplemented
217C22⋊Dic71—28no—
218C22⋊Dic71—44no—
219C22⋊Dic71C22×C4116yescomplemented
220(C2×D71)⋊C4—28no—
221(C2×D71)⋊C4—28no—
222(C2×D71)⋊C4C22×C4116yescomplemented
223C4×Dic71—28no—
224C4×Dic71—44no—
225C4×Dic71—44no—
226C24×C71—22no—
227C24×C71—22no—
228C24×C71—22no—
229C24×C71—22no—
230C24×C71—22no—
231C24×C71—22no—
232C24×C71C22×C414yes—
233C24×C71C2412yes—
234C24×C71C2411yescharacteristic
235C22×C4×C71—22no—
236C22×C4×C71—22no—
237C22×C4×C71—22no—
238C22×C4×C71—22no—
239C22×C4×C71—22no—
240C22×C4×C71—22no—
241C22×C4×C71—22no—
242C22×C4×C71—22no—
243C22×C4×C71—22no—
244C22×C4×C71—22no—
245C22×C4×C71—22no—
246C22×C4×C71—22no—
247C22×C4×C71—22no—
248C22×C4×C71—22no—
249C22×C4×C71—22no—
250C22×C4×C71—28no—
251C22×C4×C71—44no—
252C22×C4×C71—44no—
253C22×C4×C71—416no—
254C22×C4×C71C22×C414yes—
255C22×C4×C71C22×C414yes—
256C22×C4×C71C2×D414yes—
257C22×C4×C71C2412yes—
258C22×C4×C71C2412yes—
259C22×C4×C71C2412yes—
260C22×C4×C71C2412yes—
261C22×C4×C71C2412yes—
262C22×C4×C71C2412yes—
263C4⋊C4×C71—28no—
264C4⋊C4×C71—44no—
265C22⋊C4×C71—44no—
266C22⋊C4×C71C22×C4116yescomplemented
267C23×C71—28no—
268C23×C71—28no—
269C23×C71—28no—
270C23×C71—22no—
271C23×C71—22no—
272C23×C71—22no—
273C23×C71—22no—
274C23×C71—22no—
275C23×C71—22no—
276C23×C71—44no—
277C23×C71—44no—
278C23×C71—44no—
279C23×C71—44no—
280C23×C71C23×C414yes—
281C23×C71C23×C412yes—
282C23×C71C22×D412yes—
283C23×C71C2×#4112yes—
284C23×C71H(5,𝔽2)12yes—
285C23×C71H(5,𝔽2)12yes—
286C23×C712−1+412yes—
287C23×C712−1+412yes—
288C23×C71C2511yescharacteristic
289C22×D71—28no—
290C22×D71—28no—
291C22×D71—28no—
292C22×D71—28no—
293C22×D71—28no—
294C22×D71—28no—
295C22×D71—22no—
296C22×D71—22no—
297C22×D71—22no—
298C22×D71—22no—
299C22×D71C4×D4116yes—
300C22×D71C23×C414yes—
301C22×D71C22×D414yes—
302C22×D71C2×#4114yes—
303C2×C4×C71—28no—
304C2×C4×C71—28no—
305C2×C4×C71—28no—
306C2×C4×C71—22no—
307C2×C4×C71—22no—
308C2×C4×C71—22no—
309C2×C4×C71—22no—
310C2×C4×C71—22no—
311C2×C4×C71—22no—
312C2×C4×C71—22no—
313C2×C4×C71—22no—
314C2×C4×C71—22no—
315C2×C4×C71—22no—
316C2×C4×C71—22no—
317C2×C4×C71—22no—
318C2×C4×C71—22no—
319C2×C4×C71—22no—
320C2×C4×C71—22no—
321C2×C4×C71—416no—
322C2×C4×C71—44no—
323C2×C4×C71—44no—
324C2×C4×C71—44no—
325C2×C4×C71C23×C414yes—
326C2×C4×C71C23×C414yes—
327C2×C4×C71C22×D414yes—
328C22⋊D71—232no—
329C2×Dic71—28no—
330C2×Dic71—28no—
331C2×Dic71—28no—
332C2×Dic71—28no—
333C2×Dic71—22no—
334C2×Dic71—22no—
335C2×Dic71—22no—
336C2×Dic71—22no—
337C2×Dic71—22no—
338C2×Dic71—22no—
339C2×Dic71—22no—
340C2×Dic71—22no—
341C2×Dic71—22no—
342C2×Dic71—22no—
343C2×Dic71—22no—
344C2×Dic71—22no—
345C2×Dic71—22no—
346C2×Dic71—22no—
347C2×Dic71—22no—
348C2×Dic71—22no—
349C2×Dic71—22no—
350C2×Dic71—44no—
351C2×Dic71—44no—
352C2×Dic71—44no—
353C2×Dic71C23×C414yes—
354C2×Dic71C23×C414yes—
355C2×Dic71C23×C414yes—
356C2×Dic71C22×D414yes—
357C4×D71—232no—
358C4×D71—416no—
359C4×D71—416no—
360C22×C71—24no—
361C22×C71—24no—
362C22×C71—24no—
363C22×C71—416no—
364C22×C71—42no—
365C22×C71—42no—
366C22×C71—42no—
367C22×C71—42no—
368C22×C71C2×C4×D414yes—
369C22×C71#52014yes—
370C22×C71#52014yes—
371C22×C71#53414yes—
372C22×C71#53614yes—
373C22×C71#53914yes—
374C22×C71#53914yes—
375C22×C71C24×C411yescharacteristic
376C22×C71C23×D411yescharacteristic
377C22×C71C22×#4111yescharacteristic
378C22×C71C2×H(5,𝔽2)11yescharacteristic
379C22×C71C2×H(5,𝔽2)11yescharacteristic
380C22×C71C2×2−1+411yescharacteristic
381C22×C71C2×2−1+411yescharacteristic
382C2×D71—232no—
383C2×D71—24no—
384C2×D71—24no—
385C2×D71—24no—
386C2×D71—24no—
387C2×D71—24no—
388C2×D71—24no—
389C2×D71C2×C4×D418yes—
390C4×C71—24no—
391C4×C71—24no—
392C4×C71—24no—
393C4×C71—42no—
394C4×C71—42no—
395C4×C71—42no—
396Dic71—24no—
397Dic71—24no—
398Dic71—24no—
399Dic71—24no—
400Dic71—42no—
401Dic71—42no—
402Dic71—42no—
403C2×#2322—711nomaximal, Sylow
404C2×C71—44no—
405C2×C71#232218yescomplemented
406C2×C71C22×C4×D411yescharacteristic
407C2×C71C2×#52011yescharacteristic
408C2×C71C2×#52011yescharacteristic
409C2×C71C2×#53411yescharacteristic
410C2×C71C2×#53611yescharacteristic
411C2×C71C2×#53911yescharacteristic
412C2×C71C2×#53911yescharacteristic
413D71—28no—
414C22×#123—711no—
415C22×C4×D4—711no—
416C23×C4⋊C4—711no—
417#2322—7116no—
418C2×#389—711no—
419C2×#389—711no—
420C2×#388—711no—
421C2×#388—711no—
422C2×#387—711no—
423C2×#387—711no—
424C2×#386—711no—
425C2×#385—711no—
426C2×#385—711no—
427C2×#385D7111yescharacteristic, complemented
428C2×#381—711no—
429C2×C4×C22⋊C4—711no—
430C71C2×#232211yescharacteristic, complemented, Sylow
431C23×D4—711no—
432C24×C4—711no—
433C24×C4—711no—
434C24×C4—711no—
435C24×C4C2×D7111yescharacteristic
436C2×#123—7116no—
437C2×#123—718no—
438C2×C4×D4—718no—
439C2×C4×D4—1428no—
440C22×C4⋊C4—711no—
441C22×C4⋊C4—711no—
442C22×C4⋊C4—711no—
443C22×C4⋊C4—711no—
444C22×C4⋊C4—711no—
445C22×C4⋊C4—711no—
446C22×C4⋊C4—711no—
447C22×C4⋊C4—718no—
448C22×C4⋊C4—1428no—
449C22×C4⋊C4C2×D7111yescharacteristic
450C22×C4⋊C4C2×D7111yescharacteristic
451C22×C22⋊C4—711no—
452C22×C22⋊C4—711no—
453C22×C22⋊C4—711no—
454C22×C22⋊C4—711no—
455C22×C22⋊C4—711no—
456C22×C22⋊C4—711no—
457C22×C22⋊C4C2×D7111yescharacteristic
458C22×C22⋊C4C2×D7111yescharacteristic
459C22×C42—711no—
460C22×C42—711no—
461C22×C42—711no—
462#389—718no—
463#389—718no—
464#388—718no—
465#388—718no—
466#387—718no—
467#387—718no—
468#386—718no—
469#385—718no—
470#385—718no—
471#385C2×D7118yescomplemented
472#381—718no—
473C4×C22⋊C4—718no—
474C2×#95—711no—
475C2×#95—711no—
476C2×#95—711no—
477C2×#95—711no—
478C2×#95—711no—
479C2×#95—711no—
480C2×#95—711no—
481C2×#95—711no—
482C2×#95C2×D7111yescharacteristic
483C2×#95C2×D7111yescharacteristic
484C25—711no—
485C25C22×D7111yescharacteristic
486C22×D4—718no—
487C22×D4—714no—
488C22×D4—1424no—
489C22×D4—1424no—
490C23×C4—24no—
491C23×C4—42no—
492C23×C4—42no—
493C23×C4—2842no—
494C23×C4—2842no—
495C23×C4—2842no—
496C23×C4—2842no—
497C23×C4—718no—
498C23×C4—714no—
499C23×C4—714no—
500C23×C4—711no—
501C23×C4—711no—
502C23×C4—711no—
503C23×C4—711no—
504C23×C4—718no—
505C23×C4—714no—
506C23×C4—711no—
507C23×C4—711no—
508C23×C4—711no—
509C23×C4—1424no—
510C23×C4—1424no—
511C23×C4—1424no—
512C23×C4C22×D7111yescharacteristic
513C23×C4C22×D7111yescharacteristic
514C23×C4C22×D7111yescharacteristic
515C23×C4C22×D7111yescharacteristic
516C23×C4C22×D7111yescharacteristic
517C23×C4C22×D7111yescharacteristic
518C23×C4C22×D7114yes—
519#123—7164no—
520C4×D4—14232no—
521C2×C4⋊C4—24no—
522C2×C4⋊C4—42no—
523C2×C4⋊C4—2842no—
524C2×C4⋊C4—714no—
525C2×C4⋊C4—718no—
526C2×C4⋊C4—718no—
527C2×C4⋊C4—714no—
528C2×C4⋊C4—714no—
529C2×C4⋊C4—714no—
530C2×C4⋊C4—714no—
531C2×C4⋊C4—714no—
532C2×C4⋊C4—714no—
533C2×C4⋊C4—14232no—
534C2×C4⋊C4—1424no—
535C2×C4⋊C4—1424no—
536C2×C4⋊C4—1424no—
537C2×C4⋊C4—1424no—
538C2×C4⋊C4C22×D7114yes—
539C2×C4⋊C4C22×D7114yes—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—2842no—
542C2×C22⋊C4—714no—
543C2×C22⋊C4—718no—
544C2×C22⋊C4—714no—
545C2×C22⋊C4—718no—
546C2×C22⋊C4—714no—
547C2×C22⋊C4—714no—
548C2×C22⋊C4—714no—
549C2×C22⋊C4—714no—
550C2×C22⋊C4—1424no—
551C2×C22⋊C4—1424no—
552C2×C22⋊C4—1424no—
553C2×C22⋊C4C4×D7118yescomplemented
554C2×C22⋊C4C22×D7114yes—
555C2×C22⋊C4C22×D7114yes—
556C2×C42—2842no—
557C2×C42—2842no—
558C2×C42—714no—
559C2×C42—714no—
560C2×C42—714no—
561C2×C42—1424no—
562#95—714no—
563#95—714no—
564#95—714no—
565#95—714no—
566#95—714no—
567#95—714no—
568#95—714no—
569#95—714no—
570#95C22×D7114yes—
571#95C22×D7114yes—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—714no—
579C24—714no—
580C24—714no—
581C24—712no—
582C24—1422no—
583C24—1422no—
584C24—1422no—
585C24—1422no—
586C24C2×C4×D7114yes—
587C24C23×D7112yes—
588C24C23×D7111yescharacteristic
589C2×D4—7116no—
590C2×D4—1428no—
591C2×D4—1428no—
592C2×D4—14232no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—28no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—416no—
612C22×C4—2844no—
613C22×C4—2844no—
614C22×C4—28416no—
615C22×C4—2844no—
616C22×C4—2844no—
617C22×C4—28416no—
618C22×C4—7116no—
619C22×C4—714no—
620C22×C4—714no—
621C22×C4—714no—
622C22×C4—714no—
623C22×C4—712no—
624C22×C4—712no—
625C22×C4—712no—
626C22×C4—712no—
627C22×C4—7116no—
628C22×C4—712no—
629C22×C4—712no—
630C22×C4—712no—
631C22×C4—1428no—
632C22×C4—1428no—
633C22×C4—1428no—
634C22×C4—14232no—
635C22×C4—1422no—
636C22×C4—1422no—
637C22×C4—1422no—
638C22×C4—1422no—
639C22×C4—1422no—
640C22×C4—1422no—
641C22×C4—1422no—
642C22×C4—1422no—
643C22×C4—1422no—
644C22×C4—1422no—
645C22×C4—1422no—
646C22×C4—1422no—
647C22×C4—1422no—
648C22×C4—1422no—
649C22×C4—1422no—
650C22×C4—1422no—
651C22×C4—1422no—
652C22×C4C2×C4×D7114yes—
653C22×C4C2×C4×D7114yes—
654C22×C4D4×D7114yes—
655C22×C4C23×D7112yes—
656C22×C4C23×D7112yes—
657C22×C4C23×D7112yes—
658C22×C4C23×D7112yes—
659C22×C4C23×D7112yes—
660C22×C4C23×D7112yes—
661C4⋊C4—28no—
662C4⋊C4—44no—
663C4⋊C4—2844no—
664C4⋊C4—7116no—
665C4⋊C4—7116no—
666C4⋊C4—1428no—
667C4⋊C4—1428no—
668C4⋊C4—1428no—
669C4⋊C4—1428no—
670C22⋊C4—44no—
671C22⋊C4—2844no—
672C22⋊C4—7116no—
673C22⋊C4—7116no—
674C22⋊C4—1428no—
675C22⋊C4—1428no—
676C22⋊C4—1428no—
677C22⋊C4C2×C4×D71116yescomplemented
678C42—2844no—
679C42—2844no—
680C42—1428no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—28no—
688C23—28no—
689C23—28no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—714no—
695C23—714no—
696C23—714no—
697C23—7116no—
698C23—1428no—
699C23—1422no—
700C23—1422no—
701C23—1422no—
702C23—1422no—
703C23—1428no—
704C23—1428no—
705C23—1428no—
706C23—1428no—
707C23—1428no—
708C23C22×C4×D7114yes—
709C23C22×C4×D7112yes—
710C23C2×D4×D7112yes—
711C23#41×D7112yes—
712C23#1455617312yes—
713C23#1455617312yes—
714C23#1455617512yes—
715C23#1455617612yes—
716C23C24×D7111yescharacteristic
717D4—14232no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—28no—
725C2×C4—28no—
726C2×C4—28no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—416no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—28416no—
741C2×C4—28416no—
742C2×C4—2844no—
743C2×C4—2844no—
744C2×C4—2844no—
745C2×C4—714no—
746C2×C4—714no—
747C2×C4—714no—
748C2×C4—714no—
749C2×C4—14232no—
750C2×C4—1422no—
751C2×C4—1422no—
752C2×C4—1422no—
753C2×C4—1422no—
754C2×C4—1422no—
755C2×C4—1422no—
756C2×C4—1422no—
757C2×C4—1422no—
758C2×C4—1422no—
759C2×C4—1422no—
760C2×C4—1422no—
761C2×C4—1422no—
762C2×C4—1422no—
763C2×C4—1422no—
764C2×C4—1422no—
765C2×C4—1422no—
766C2×C4—1422no—
767C2×C4—1428no—
768C2×C4—1428no—
769C2×C4—1428no—
770C2×C4—1428no—
771C2×C4C22×C4×D7114yes—
772C2×C4C22×C4×D7114yes—
773C2×C4C2×D4×D7114yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—416no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—718no—
783C22—14232no—
784C22—1424no—
785C22—1424no—
786C22—1424no—
787C22—1424no—
788C22—1424no—
789C22—1424no—
790C22C4×D4×D7114yes—
791C22#1798647814yes—
792C22#1798648014yes—
793C22#1798655914yes—
794C22#1798657214yes—
795C22#1798659214yes—
796C22#1798659514yes—
797C22C23×C4×D7111yescharacteristic
798C22C22×D4×D7111yescharacteristic
799C22C2×#41×D7111yescharacteristic
800C22C2×#1455617311yescharacteristic
801C22C2×#1455617311yescharacteristic
802C22C2×#1455617511yescharacteristic
803C22C2×#1455617611yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—2842no—
811C4—2842no—
812C4—2842no—
813C4—1424no—
814C4—1424no—
815C4—1424no—
816C4—1424no—
817C2—44no—
818C2—1428no—
819C2#2259100718yesdirect product factor
820C2C2×C4×D4×D7111yescharacteristic
821C2C2×#1798647811yescharacteristic
822C2C2×#1798648011yescharacteristic
823C2C2×#1798655911yescharacteristic
824C2C2×#1798657211yescharacteristic
825C2C2×#1798659211yescharacteristic
826C2C2×#1798659511yescharacteristic
subgroupG/H
centerC24C23×D71
commutatorC22×C71C24×C4
FrattiniC23C24×D71
FittingC2×#385×C71C2
socleC24×C71C24
prime radicalC23×C22⋊D71C22
cosocleC23×C71C25
hypercenterC2×#385D71
hypocenterC71C2×#2322
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#385

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C22×C4⋊C4×D71C2semidirect
4. #22591007C2direct (N × H)
5. C2×#17985896C2semidirect
6. C2×#17985895C2semidirect
7. C2×#17985892C2semidirect
8. C2×#17985887C2semidirect
9. C2×#17985884C2semidirect
10. C2×#17985880C2semidirect
12. C2×#17985872C2semidirect
13. C2×#17985870C2semidirect
14. C2×#17985861C2semidirect
15. C2×#17985846C2semidirect
16. C2×#385×C71C2semidirect
21. C2×#14556110C4semidirect
33. C2×C4⋊C4×D71C22semidirect
43. #17985896C22semidirect
44. #17985895C22semidirect
45. #17985892C22semidirect
46. #17985887C22semidirect
47. #17985884C22semidirect
48. #17985880C22semidirect
50. #17985872C22semidirect
51. #17985870C22semidirect
52. #17985861C22semidirect
53. #17985846C22semidirect
67. #385×C71C22semidirect
89. C22×C4×D71C2×C4semidirect
94. #14556110C2×C4semidirect
97. C2×C4⋊Dic71C2×C4semidirect
104. C2×Dic71⋊C4C2×C4semidirect
113. C2×C22⋊Dic71C2×C4semidirect
119. C2×(C2×D71)⋊C4C2×C4semidirect
153. C2×C22⋊C4×C71C2×C4semidirect
208. C2×C4×D71C22×C4semidirect
211. C4⋊Dic71C22×C4semidirect
216. Dic71⋊C4C22×C4semidirect
219. C22⋊Dic71C22×C4semidirect
222. (C2×D71)⋊C4C22×C4semidirect
266. C22⋊C4×C71C22×C4semidirect
405. C2×C71#2322semidirect
427. C2×#385D71semidirect
430. C71C2×#2322semidirect
471. #385C2×D71semidirect
553. C2×C22⋊C4C4×D71semidirect
677. C22⋊C4C2×C4×D71semidirect
819. C2#22591007direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#145561102
C22×C4×C22⋊D712
C22×C4⋊C4×D712
#225910072
C2×#179858962
C2×#179858952
C2×#179858922
C2×#179858872
C2×#179858842
C2×#179858802
C2×#179858752
C2×#179858722
C2×#179858702
C2×#179858612
C2×#179858462
C2×#385×C712
C2×#232271